Motions of particles around black holes, especially in their equatorial planes, attract much attention. The reason is that these motions convey important information on the background spacetimes. For example, null geodesics are useful to explain quasinormal modes (QNMs) of a black hole. The real part of QNMs is determined by the angular velocity of a particle at the unstable orbit, and the imaginary part is related to the unstable timescale of the orbit [1]}. Unstable circular geodesics affect the optical appearance of a gravitationally collapsed star, and then can explain the star's luminosity [2]}. Moreover, the spins and merger of black holes can also be explained by circular motions of particles [3]}.
